Modeling correlated motion in thermoelectric skutterudite materials

Filled skutterudite compounds, LnT$_{4}$X$_{12}$ (Ln=rare earth; T=Fe,Ru,Os; X=P,As,Sb), have previously been modeled using a rigid cage approximation for the ``rattling'' rare earth atom. The large thermal broadening with temperature of the rattler can be fit using an Einstein model. Recent measurements of the second neighbor Ln-T peaks show an unusually large thermal broadening suggesting motion of the cage of atoms. To incorporate these results we developed three and four mass spring models to give the acoustic and optical phonon mode spectra. For the simplest three mass model we identify the low energy optical mode as the rattling mode. This rattling mode is likely coupled to the acoustic mode, and responsible for the low thermal conductivity of the skutterudite compound. We extend this model to four atoms to describe the CuO$_{4}$ rings in oxy-skutterudites and the X$_{4}$ rings in LnT$_{4}$X$_{12}$. This talk provides a model for the experimental results of the previous presentation.